# Research

I am currently working under the mentorship of Dr. David P. Herzog. We study the asymptotic stability of nonlinear stochastic dynamics. Our most recent pre-print establishes explicit rates of convergence for Langevin dynamics subject to singular potentials in a weighted norm. More recently, we are focusing on the asymptotic behavior of degenerately stochastically forced Lorenz 96 systems.

My mathematical research and interests lie in:

Stochastic Processes

Chaos Theory and Nonlinear Dynamics

Functional Analysis

Partial Differential Equations

Quantum Mechanics

Mathematical Chemistry

## A recent presentation of our Langevin dynamics results.

# Research with Undergraduates

I was privileged enough to participate in mathematics research as an undergraduate at Concordia College, as well as through an NSF-funded research program at New York University. These experiences were invaluable to my future career as a mathematician, and I try to participate in leading undergraduate research whenever possible. The list of program topics I have led with undergraduates includes:

Fractals and iterated function systems

Sampling and interpolation theory

Markov chains and mixing times

Models for turbulent flow

Semigroup theory

Fractional operator theory

Selected Publications:

Weighted L2-contractivity of Langevin dynamics with singular potentials

Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]

Stability of the Kaczmarz reconstruction for stationary sequences

On the nature of the conformable derivative and its applications to physics

A tractable numerical model for exploring nonadiabatic quantum dynamics

Links to my research profiles: